Unit #11: Arcs and Angles in Circles

Circle Terminology

Circle Formulas

“Central” Station

“Inscribed” Station

“Interior” Station

Exterior Angles/BIG Circle

Unit #11 Test Review

Diameter: Radius:

Inscribed Angle: Central Angle:

Intercepted Arc: Major Arc:

Minor Arc: Chord:

Secant: Tangent:

Central Angle: Inscribed Angle:

(OR Tangent Chord Angle):

Interior Angle:

Exterior Angle:

“Central” Station: 1) Given the diagram find the measure of:

2) Given: Circle A, solve for x. 3) Given: Circle O, solve for x and y.

62O

“Inscribed” Station:

1) Given: Diameter AOB 2) Given: Circle O, tangent BA , chord .AC

3) Given: Chords AB and BC 4) Given: Diameter AOB

5) Given: Circle A 6) Given: Diameter AOB

“Interior” Station:

1) Given: Chords AB and CD 2) Given: Chords AB and CD Solve for x. Solve for x.

** 3) Solve for X: 4) Chords MN and PQ intersect at

point R in circle O. If mMQ = 112 and

mPN =80, what is the measure of

m MRQ ?

5) In circle O, chords CH and AD intersect at point Q inside the circle. If m AQH = 51 and

mCD = 64 find the mAH .

Name: _________________________________ Day __ Per __

Geometry Lab Exterior <

Formula:

1) From an external point, two tangents are drawn to a circle. If the tangent intercepts a major arc of

204o, what is the measure of the angle formed by the tangents?

2) Solve for x: 3) Solve for x:

4) Solve for X: 5) Solve for X:

6) Solve for X: 7) Solve for X:

8) Solve for X:

The BIG Circle Question 9)

: 60 ; 40; 2 16,

' 1 12

OGiven CircleO withtangent MN and mSN mQP x mPN x SQ x

find themeasures of s

Name:_________________________________ Day __ Per __

Geometry Lab Unit #11: Circle Test Review

1) Given: circle Z with MA//RG, MA≅GR 2) Find the measure of <MAZ

Find the mGR .

3) In the accompanying diagram, IP and PG 4) Solve for x.

are tangent to circle M from point P.

If m<IPG = 63o find m<I

5) Find x 6) CD is the altitude to the

hypotenuse AB of rt. ABC. Find the

length of AD if AC=6 and AB = 10

7) Given ABC, with centroid E, 8) In MAT, H and S are midpoints.

if AF=18, find AE. If the slope of HS =1

2, what if the slope of

TA? If m<MSH = 12x+28 and the

m<MAT = 16x-40, find <MSH.

9) Given the statement: “If I see flowers blooming, then it is not winter.”

Write the following:

a) Inverse:

b) Converse:

c) Contrapositive:

d) Which of the above is logically equivalent to the original statement?

10) The endpoints of CD are C (-2a,-4b) and D (6a, 2b).

a) Find the midpoint of CD? b) Find the slope of CD?

11) Write the equation of the line that contains the point (3,-1) and is perpendicular to the

line 3x +2y = 2.

12) The coordinates of the midpoint of AB are (2,4), and the coordinates of point B are

(3,7). What are the coordinates of point A?

13) Given: PA//UE

Prove: PQ x UQ = EQ x AQ

14) Given circle O with Tangent DE and

Find the measure of each numbered angle.

D